Armature not moving mesh properly?
Despite the fact that the hand is completely red, it is still most likely a weight painting issue.

A vertex on a mesh can be assigned to multiple different vertex groups which means it can be affected by multiple different bones. Since the hand mesh looks to be moving about half as much as it should, I think you have the vertices assigned to a second group as well.

You can manually select the bones in weight paint mode to see which one is causing the issue, but there is a quick way to solve this without even knowing which bone is the culprit.

In the vertex groups panel of the Object Data tab of the properties panel there is a small, dark arrow pointing down located on the right side (under the Plus and Minus icons). With your hand vertices selected, click on it to open a menu, and choose the Remove from All Groups option. 



This will remove any and all vertex groups from these vertices. Then select the hand vertex group  and assign a weight of 1 to your hand vertices and you should be good to go.